In a family of two children, find the probability that the family has two boys given that the first child is a boy.
that's the same as asking what's the chance of the 2nd child being a boy.
To find the probability that a family with two children has two boys given that the first child is a boy, we can use conditional probability.
Let's start by enumerating all the possible outcomes of this scenario based on the gender of the two children:
- Boy, Boy (BB)
- Boy, Girl (BG)
- Girl, Boy (GB)
- Girl, Girl (GG)
In this case, we know that the first child is a boy. So, we can eliminate the fourth possibility (GG) since it is impossible.
Now, we are left with three possible outcomes, out of which only one has two boys (BB). Thus, the probability of having two boys given that the first child is a boy is 1 out of 3.
So, the probability is 1/3 or approximately 0.3333.